Domain of Euler Mean in the Space of Absolutely p-Summable Double Sequences with 0 ＜ p ＜ 1

摘要

In this study,as the domain of four dimensional Euler mean E(r,s) of ordersr,s in the space Lp for 0 ＜ p ＜ 1,we examine the double sequence space εr,sp and some properties of four dimensional Euler mean.We determine the α-and β(bp)-duals of the space εp,and characterize the classes (εr,sp∶ Mu),(εr,sp ∶ ebp) and (εr,sp ∶ L q) of four dimensional matrix transformations,where 1 ≤ q ＜ ∞.Finally,we shortly emphasize on the Euler spaces of single and double sequences,and note some further suggestions.